Just How Nepotistic Are We?

THERE is a very real chance that the presidential election in 2016 will pit Jeb Bush against Hillary Clinton. According to oddsmakers, this is the likeliest outcome.

Many Americans are uncomfortable with the idea that two families could dominate the presidency that way. Whether or not you like one of the candidates, it just doesn’t feel right, in part because a second Bush-Clinton election makes a mockery of our self-identification as a democratic meritocracy.

How bad is America’s nepotism problem? Can data science help us gauge its depth? It can — and what the data shows is that something has gone haywire.

I studied the probability of male baby boomers’ reaching the same level of success as their fathers. I had to limit myself to fathers and sons because this was a highly sexist period in which women held few powerful political positions.

Let’s start with the presidency. Thirteen sons of presidents were born during America’s baby boom. One of the 13 became president himself, of course, and Jeb would make a second. Of the roughly 37 million boomer males who weren’t born to a president, two won the White House. Maybe it’s an anomaly that George W. Bush became president in 2001, but his advent means that in our era a son of a president was roughly 1.4 million times more likely to become president than his supposed peers.

The presidency is obviously a small sample. But the same calculations can be done for other political positions. Take governors.

Because it is difficult to be sure that you have counted all the sons of governors, let’s assume that governors reproduce at average rates. This would mean there were about 250 baby boomer males born to governors. Five of them became governors themselves, about one in 50. This is 6,000 times the rate of the average American. The same methodology suggests that sons of senators had an 8,500 times higher chance of becoming a senator than an average American male boomer.

There is some evidence that the parental advantage in politics is actually getting bigger. George W. Bush ended a 171-year drought for presidential sons. From 2003 to 2006, the Senate had the highest percentage of senators’ children — six — in its history.

Is this electoral edge unusual? Successful parents, whatever their occupation, pass on their genes and plenty of other stuff to their kids. Do different fields have similar familial patterns?

In just about every field I looked at, having a successful parent makes you way more likely to be a big success, but the advantage is much smaller than it is at the top of politics.

Using the same methodology, I estimate that the son of an N.B.A. player has about a one in 45 chance of becoming an N.B.A. player. Since there are far more N.B.A. slots than Senate slots, this is only about an 800-fold edge.

Think about the N.B.A. further. The skills necessary to be a basketball player, especially height, are highly hereditary. But the N.B.A. is a meritocracy, with your performance easy to evaluate. If you do not play well, you will be cut, even if the team is the New York Knicks and your name is Patrick Ewing Jr. Father-son correlation in the N.B.A. is only one-eleventh as high as it is in the Senate.

The parental edge in football and baseball is much lower than it is in basketball, probably because there is less reliance on height.

I went through a wide range of fields and found a consistent pattern: greater success for the sons, but nothing like the edge a winning politician provides.

Here is the estimated parental edge for other big American prizes and positions. An American male is 4,582 times more likely to become an Army general if his father was one; 1,895 times more likely to become a famous C.E.O.; 1,639 times more likely to win a Pulitzer Prize; 1,497 times more likely to win a Grammy; and 1,361 times more likely to win an Academy Award. Those are pretty decent odds, but they do not come close to the 8,500 times more likely a senator’s son is to find himself chatting with John McCain or Dianne Feinstein in the Senate cloakroom.

THE Bush story is also telling, when we compare it to familial success in other fields.

Has any modern family dominated a meritocracy the way that the Bushes dominate politics? I could not find one. The Mannings, in football, probably come closest. But while Archie Manning, the father of two Super Bowl-winning quarterbacks, Peyton and Eli, was a solid N.F.L. player, he was hardly the football equivalent of a president.

Internationally, the greatest father-son, merit-based, same-field accomplishment is probably Niels Bohr’s son Aage matching his father’s Nobel Prize in Physics. But neither the Bohrs nor the Mannings dominated physics or football the way the Bush family dominates American politics.

Regression to the mean limits family dominance in any meritocratic field. If you have a well-above-average dose of a trait, you can expect your child to be closer to average.

Regression to the mean is so powerful that once-in-a-generation talent basically never sires once-in-a-generation talent. It explains why Michael Jordan’s sons were middling college basketball players and Jakob Dylan wrote two good songs. It is why there are no American parent-child pairs among Hall of Fame players in any major professional sports league.

The Bush family’s dominance would be the basketball equivalent of Michael Jordan being the father of LeBron James and Kevin Durant — and of Michael Jordan’s father being Walt Frazier.

In other words, it is virtually impossible, statistically speaking, that Bushes are consistently the most talented people to lead our country. Same for Chelsea Clinton or any other member of a political dynasty thought to be possible presidential timber.

Politics is not the absolute worst field in giving an advantage to certain families. In my research, I found two fields with a bigger family edge.

First is billionaires. According to my calculation, you have about a 28,000 times higher chance of being a billionaire if your father was a billionaire. And billionaires like the Waltons or the Rockefellers before them probably dominate American wealth more than the Bushes dominate American politics.

These billionaires, of course, have inherited their status, not earned it. Call me jaded, but it seems to me that most heirs to billionaires don’t do much more than marry nice-looking people and take sports franchises that I support and run them into the ground.

The second group is reality TV stars. You have about a 9,300 times edge in becoming a reality television star if your father is one. But this is precisely because some of these shows star famous people’s families.

We should not take this criticism too far. In 2008, the United States chose the mixed-race son of a Kenyan and a Kansan to be president. More than 90 percent of senators had parents who weren’t top politicians. And political campaigns can be unpredictable. For all we know, the 2016 election could be fought between Senator Elizabeth Warren, daughter of a janitor, and Gov. Scott Walker, son of a minister.

Unless of course the Democratic candidate is Andrew M. Cuomo, son of a governor, and the Republican candidate is Rand Paul, son of a congressman.

There are plenty of countries that are worse. Over the past 50 years, being the son of a leader of North Korea increased your probability of being a leader of North Korea by a factor of infinity. An infinite advantage to having a powerful father has been common in human history.

But Big Data allows us not just vague comparisons to other countries or time periods. We can see precisely how much families dominate in many different spheres and we can see what true meritocracies look like. The data shows conclusively that we have a nepotism problem. So now the question is: Why does the modern United States tolerate this level of privilege for political name brands?

Correction:March 29, 2015

A cover opinion essay last Sunday, about nepotism in America, incorrectly asserted that there were no American parent-child pairs among Nobel Prize winners. In fact, Arthur Kornberg won a Nobel Prize in Medicine in 1959, and his son Roger D. Kornberg won a Nobel Prize in Chemistry in 2006.

Seth Stephens-Davidowitz is an economist and a contributing opinion writer.